1. A relation that provides the foundation for something
   "he worked on an interim basis";
   - footing, ground
    
2. The fundamental assumptions from which something is begun, developed, calculated or explained
   "the whole argument rested on a basis of conjecture";
   - base, foundation, fundament, groundwork, cornerstone
    
3. The most important or necessary part of something
   "the basis of this drink is orange juice";
   - base
    
4. (mathematics) in a vector space, a linearly independent set of vectors spanning the whole vector space
   "The standard basis for 3D space consists of three unit vectors along the x, y, and z axes"

Type of: assumption, component, component part, constituent, foundation, part, portion, supposal, supposition

Part of: explanation

Encyclopedia: Basis